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<!doctype html> <html lang="en" class="no-js"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width,initial-scale=1"> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="description" content="API Reference Documentation for FreeType-2.10.4"> <meta name="author" content="FreeType Contributors"> <meta name="lang:clipboard.copy" content="Copy to clipboard"> <meta name="lang:clipboard.copied" content="Copied to clipboard"> <meta name="lang:search.language" content="en"> <meta name="lang:search.pipeline.stopwords" content="True"> <meta name="lang:search.pipeline.trimmer" content="True"> <meta name="lang:search.result.none" content="No matching documents"> <meta name="lang:search.result.one" content="1 matching document"> <meta name="lang:search.result.other" content="# matching documents"> <meta name="lang:search.tokenizer" content="[\s\-]+"> <link rel="shortcut icon" href="images/favico.ico"> <meta name="generator" content="mkdocs-1.1, 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Sub-System </label> <nav class="md-nav" data-md-component="collapsible" data-md-level="1"> <label class="md-nav__title" for="nav-7"> Cache Sub-System </label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item"> <a href="ft2-cache_subsystem.html" title="Cache Sub-System" class="md-nav__link"> Cache Sub-System </a> </li> </ul> </nav> </li> <li class="md-nav__item md-nav__item--active md-nav__item--nested"> <input class="md-toggle md-nav__toggle" data-md-toggle="nav-8" type="checkbox" id="nav-8" checked> <label class="md-nav__link" for="nav-8"> Support API </label> <nav class="md-nav" data-md-component="collapsible" data-md-level="1"> <label class="md-nav__title" for="nav-8"> Support API </label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item md-nav__item--active"> <input class="md-toggle md-nav__toggle" data-md-toggle="toc" type="checkbox" id="__toc"> <label class="md-nav__link md-nav__link--active" for="__toc"> Computations </label> <a href="ft2-computations.html" title="Computations" class="md-nav__link md-nav__link--active"> Computations </a> <nav class="md-nav md-nav--secondary"> <label class="md-nav__title" for="__toc">Table of contents</label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item"> <a href="#synopsis" class="md-nav__link"> Synopsis </a> </li> <li class="md-nav__item"> <a href="#ft_muldiv" class="md-nav__link"> FT_MulDiv </a> </li> <li class="md-nav__item"> <a href="#ft_mulfix" class="md-nav__link"> FT_MulFix </a> </li> <li class="md-nav__item"> <a href="#ft_divfix" class="md-nav__link"> FT_DivFix </a> </li> <li class="md-nav__item"> <a href="#ft_roundfix" class="md-nav__link"> FT_RoundFix </a> </li> <li class="md-nav__item"> <a href="#ft_ceilfix" class="md-nav__link"> FT_CeilFix </a> </li> <li class="md-nav__item"> <a href="#ft_floorfix" class="md-nav__link"> FT_FloorFix </a> </li> <li class="md-nav__item"> <a href="#ft_vector_transform" class="md-nav__link"> FT_Vector_Transform </a> </li> <li class="md-nav__item"> <a href="#ft_matrix_multiply" class="md-nav__link"> FT_Matrix_Multiply </a> </li> <li class="md-nav__item"> <a href="#ft_matrix_invert" class="md-nav__link"> FT_Matrix_Invert </a> </li> <li class="md-nav__item"> <a href="#ft_angle" class="md-nav__link"> FT_Angle </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi" class="md-nav__link"> FT_ANGLE_PI </a> </li> <li class="md-nav__item"> <a href="#ft_angle_2pi" class="md-nav__link"> FT_ANGLE_2PI </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi2" class="md-nav__link"> FT_ANGLE_PI2 </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi4" class="md-nav__link"> FT_ANGLE_PI4 </a> </li> <li class="md-nav__item"> <a href="#ft_sin" class="md-nav__link"> FT_Sin </a> </li> <li class="md-nav__item"> <a href="#ft_cos" class="md-nav__link"> FT_Cos </a> </li> <li class="md-nav__item"> <a href="#ft_tan" class="md-nav__link"> FT_Tan </a> </li> <li class="md-nav__item"> <a href="#ft_atan2" class="md-nav__link"> FT_Atan2 </a> </li> <li class="md-nav__item"> <a href="#ft_angle_diff" class="md-nav__link"> FT_Angle_Diff </a> </li> <li class="md-nav__item"> <a href="#ft_vector_unit" class="md-nav__link"> FT_Vector_Unit </a> </li> <li class="md-nav__item"> <a href="#ft_vector_rotate" class="md-nav__link"> FT_Vector_Rotate </a> </li> <li class="md-nav__item"> <a href="#ft_vector_length" class="md-nav__link"> FT_Vector_Length </a> </li> <li class="md-nav__item"> <a href="#ft_vector_polarize" class="md-nav__link"> FT_Vector_Polarize </a> </li> <li class="md-nav__item"> <a href="#ft_vector_from_polar" class="md-nav__link"> FT_Vector_From_Polar </a> </li> </ul> </nav> </li> <li class="md-nav__item"> <a href="ft2-list_processing.html" title="List Processing" class="md-nav__link"> List Processing </a> </li> <li class="md-nav__item"> <a href="ft2-outline_processing.html" title="Outline Processing" class="md-nav__link"> Outline Processing </a> </li> <li class="md-nav__item"> <a href="ft2-quick_advance.html" title="Quick retrieval of advance values" class="md-nav__link"> Quick retrieval of advance values </a> </li> <li class="md-nav__item"> <a href="ft2-bitmap_handling.html" title="Bitmap Handling" class="md-nav__link"> Bitmap Handling </a> </li> <li class="md-nav__item"> <a href="ft2-raster.html" title="Scanline Converter" class="md-nav__link"> Scanline Converter </a> </li> <li class="md-nav__item"> <a href="ft2-glyph_stroker.html" title="Glyph Stroker" class="md-nav__link"> Glyph Stroker </a> </li> <li class="md-nav__item"> <a href="ft2-system_interface.html" title="System Interface" class="md-nav__link"> System Interface </a> </li> <li class="md-nav__item"> <a href="ft2-module_management.html" title="Module Management" class="md-nav__link"> Module Management </a> </li> <li class="md-nav__item"> <a href="ft2-gzip.html" title="GZIP Streams" class="md-nav__link"> GZIP Streams </a> </li> <li class="md-nav__item"> <a href="ft2-lzw.html" title="LZW Streams" class="md-nav__link"> LZW Streams </a> </li> <li class="md-nav__item"> <a href="ft2-bzip2.html" title="BZIP2 Streams" class="md-nav__link"> BZIP2 Streams </a> </li> </ul> </nav> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-toggle md-nav__toggle" data-md-toggle="nav-9" type="checkbox" id="nav-9"> <label class="md-nav__link" for="nav-9"> Error Codes </label> <nav class="md-nav" data-md-component="collapsible" data-md-level="1"> <label class="md-nav__title" for="nav-9"> Error Codes </label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item"> <a href="ft2-error_enumerations.html" title="Error Enumerations" class="md-nav__link"> Error Enumerations </a> </li> <li class="md-nav__item"> <a href="ft2-error_code_values.html" title="Error Code Values" class="md-nav__link"> Error Code Values </a> </li> </ul> </nav> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-toggle md-nav__toggle" data-md-toggle="nav-10" type="checkbox" id="nav-10"> <label class="md-nav__link" for="nav-10"> Miscellaneous </label> <nav class="md-nav" data-md-component="collapsible" data-md-level="1"> <label class="md-nav__title" for="nav-10"> Miscellaneous </label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item"> <a href="ft2-gx_validation.html" title="TrueTypeGX/AAT Validation" class="md-nav__link"> TrueTypeGX/AAT Validation </a> </li> <li class="md-nav__item"> <a href="ft2-incremental.html" title="Incremental Loading" class="md-nav__link"> Incremental Loading </a> </li> <li class="md-nav__item"> <a href="ft2-truetype_engine.html" title="The TrueType Engine" class="md-nav__link"> The TrueType Engine </a> </li> <li class="md-nav__item"> <a href="ft2-ot_validation.html" title="OpenType Validation" class="md-nav__link"> OpenType Validation </a> </li> </ul> </nav> </li> </ul> </nav> </div> </div> </div> <div class="md-sidebar md-sidebar--secondary" data-md-component="toc"> <div class="md-sidebar__scrollwrap"> <div class="md-sidebar__inner"> <nav class="md-nav md-nav--secondary"> <label class="md-nav__title" for="__toc">Table of contents</label> <ul class="md-nav__list" data-md-scrollfix> <li class="md-nav__item"> <a href="#synopsis" class="md-nav__link"> Synopsis </a> </li> <li class="md-nav__item"> <a href="#ft_muldiv" class="md-nav__link"> FT_MulDiv </a> </li> <li class="md-nav__item"> <a href="#ft_mulfix" class="md-nav__link"> FT_MulFix </a> </li> <li class="md-nav__item"> <a href="#ft_divfix" class="md-nav__link"> FT_DivFix </a> </li> <li class="md-nav__item"> <a href="#ft_roundfix" class="md-nav__link"> FT_RoundFix </a> </li> <li class="md-nav__item"> <a href="#ft_ceilfix" class="md-nav__link"> FT_CeilFix </a> </li> <li class="md-nav__item"> <a href="#ft_floorfix" class="md-nav__link"> FT_FloorFix </a> </li> <li class="md-nav__item"> <a href="#ft_vector_transform" class="md-nav__link"> FT_Vector_Transform </a> </li> <li class="md-nav__item"> <a href="#ft_matrix_multiply" class="md-nav__link"> FT_Matrix_Multiply </a> </li> <li class="md-nav__item"> <a href="#ft_matrix_invert" class="md-nav__link"> FT_Matrix_Invert </a> </li> <li class="md-nav__item"> <a href="#ft_angle" class="md-nav__link"> FT_Angle </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi" class="md-nav__link"> FT_ANGLE_PI </a> </li> <li class="md-nav__item"> <a href="#ft_angle_2pi" class="md-nav__link"> FT_ANGLE_2PI </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi2" class="md-nav__link"> FT_ANGLE_PI2 </a> </li> <li class="md-nav__item"> <a href="#ft_angle_pi4" class="md-nav__link"> FT_ANGLE_PI4 </a> </li> <li class="md-nav__item"> <a href="#ft_sin" class="md-nav__link"> FT_Sin </a> </li> <li class="md-nav__item"> <a href="#ft_cos" class="md-nav__link"> FT_Cos </a> </li> <li class="md-nav__item"> <a href="#ft_tan" class="md-nav__link"> FT_Tan </a> </li> <li class="md-nav__item"> <a href="#ft_atan2" class="md-nav__link"> FT_Atan2 </a> </li> <li class="md-nav__item"> <a href="#ft_angle_diff" class="md-nav__link"> FT_Angle_Diff </a> </li> <li class="md-nav__item"> <a href="#ft_vector_unit" class="md-nav__link"> FT_Vector_Unit </a> </li> <li class="md-nav__item"> <a href="#ft_vector_rotate" class="md-nav__link"> FT_Vector_Rotate </a> </li> <li class="md-nav__item"> <a href="#ft_vector_length" class="md-nav__link"> FT_Vector_Length </a> </li> <li class="md-nav__item"> <a href="#ft_vector_polarize" class="md-nav__link"> FT_Vector_Polarize </a> </li> <li class="md-nav__item"> <a href="#ft_vector_from_polar" class="md-nav__link"> FT_Vector_From_Polar </a> </li> </ul> </nav> </div> </div> </div> <div class="md-content"> <article class="md-content__inner md-typeset"> <p><a href="https://www.freetype.org">FreeType</a> » <a href="../">Docs</a> » <a href="index.html#support-api">Support API</a> » Computations</p> <hr /> <h1 id="computations">Computations<a class="headerlink" href="#computations" title="Permanent link">¶</a></h1> <h2 id="synopsis">Synopsis<a class="headerlink" href="#synopsis" title="Permanent link">¶</a></h2> <p>This section contains various functions used to perform computations on 16.16 fixed-float numbers or 2d vectors.</p> <p><strong>Attention</strong>: Most arithmetic functions take <code>FT_Long</code> as arguments. For historical reasons, FreeType was designed under the assumption that <code>FT_Long</code> is a 32-bit integer; results can thus be undefined if the arguments don't fit into 32 bits.</p> <h2 id="ft_muldiv">FT_MulDiv<a class="headerlink" href="#ft_muldiv" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> ) <b>FT_MulDiv</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a, <a href="ft2-basic_types.html#ft_long">FT_Long</a> b, <a href="ft2-basic_types.html#ft_long">FT_Long</a> c ); </code></pre></div> <p>Compute <code>(a*b)/c</code> with maximum accuracy, using a 64-bit intermediate integer whenever necessary.</p> <p>This function isn't necessarily as fast as some processor-specific operations, but is at least completely portable.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The first multiplier.</p> </td></tr> <tr><td class="val" id="b">b</td><td class="desc"> <p>The second multiplier.</p> </td></tr> <tr><td class="val" id="c">c</td><td class="desc"> <p>The divisor.</p> </td></tr> </table> <h4>return</h4> <p>The result of <code>(a*b)/c</code>. This function never traps when trying to divide by zero; it simply returns ‘MaxInt’ or ‘MinInt’ depending on the signs of <code>a</code> and <code>b</code>.</p> <hr> <h2 id="ft_mulfix">FT_MulFix<a class="headerlink" href="#ft_mulfix" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> ) <b>FT_MulFix</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a, <a href="ft2-basic_types.html#ft_long">FT_Long</a> b ); </code></pre></div> <p>Compute <code>(a*b)/0x10000</code> with maximum accuracy. Its main use is to multiply a given value by a 16.16 fixed-point factor.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The first multiplier.</p> </td></tr> <tr><td class="val" id="b">b</td><td class="desc"> <p>The second multiplier. Use a 16.16 factor here whenever possible (see note below).</p> </td></tr> </table> <h4>return</h4> <p>The result of <code>(a*b)/0x10000</code>.</p> <h4>note</h4> <p>This function has been optimized for the case where the absolute value of <code>a</code> is less than 2048, and <code>b</code> is a 16.16 scaling factor. As this happens mainly when scaling from notional units to fractional pixels in FreeType, it resulted in noticeable speed improvements between versions 2.x and 1.x.</p> <p>As a conclusion, always try to place a 16.16 factor as the <em>second</em> argument of this function; this can make a great difference.</p> <hr> <h2 id="ft_divfix">FT_DivFix<a class="headerlink" href="#ft_divfix" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> ) <b>FT_DivFix</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a, <a href="ft2-basic_types.html#ft_long">FT_Long</a> b ); </code></pre></div> <p>Compute <code>(a*0x10000)/b</code> with maximum accuracy. Its main use is to divide a given value by a 16.16 fixed-point factor.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The numerator.</p> </td></tr> <tr><td class="val" id="b">b</td><td class="desc"> <p>The denominator. Use a 16.16 factor here.</p> </td></tr> </table> <h4>return</h4> <p>The result of <code>(a*0x10000)/b</code>.</p> <hr> <h2 id="ft_roundfix">FT_RoundFix<a class="headerlink" href="#ft_roundfix" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_RoundFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a ); </code></pre></div> <p>Round a 16.16 fixed number.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The number to be rounded.</p> </td></tr> </table> <h4>return</h4> <p><code>a</code> rounded to the nearest 16.16 fixed integer, halfway cases away from zero.</p> <h4>note</h4> <p>The function uses wrap-around arithmetic.</p> <hr> <h2 id="ft_ceilfix">FT_CeilFix<a class="headerlink" href="#ft_ceilfix" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_CeilFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a ); </code></pre></div> <p>Compute the smallest following integer of a 16.16 fixed number.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The number for which the ceiling function is to be computed.</p> </td></tr> </table> <h4>return</h4> <p><code>a</code> rounded towards plus infinity.</p> <h4>note</h4> <p>The function uses wrap-around arithmetic.</p> <hr> <h2 id="ft_floorfix">FT_FloorFix<a class="headerlink" href="#ft_floorfix" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_FloorFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a ); </code></pre></div> <p>Compute the largest previous integer of a 16.16 fixed number.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>The number for which the floor function is to be computed.</p> </td></tr> </table> <h4>return</h4> <p><code>a</code> rounded towards minus infinity.</p> <hr> <h2 id="ft_vector_transform">FT_Vector_Transform<a class="headerlink" href="#ft_vector_transform" title="Permanent link">¶</a></h2> <p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Vector_Transform</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vector, <span class="keyword">const</span> <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* matrix ); </code></pre></div> <p>Transform a single vector through a 2x2 matrix.</p> <h4>inout</h4> <table class="fields"> <tr><td class="val" id="vector">vector</td><td class="desc"> <p>The target vector to transform.</p> </td></tr> </table> <h4>input</h4> <table class="fields"> <tr><td class="val" id="matrix">matrix</td><td class="desc"> <p>A pointer to the source 2x2 matrix.</p> </td></tr> </table> <h4>note</h4> <p>The result is undefined if either <code>vector</code> or <code>matrix</code> is invalid.</p> <hr> <h2 id="ft_matrix_multiply">FT_Matrix_Multiply<a class="headerlink" href="#ft_matrix_multiply" title="Permanent link">¶</a></h2> <p>Defined in FT_GLYPH_H (freetype/ftglyph.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Matrix_Multiply</b>( <span class="keyword">const</span> <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* a, <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* b ); </code></pre></div> <p>Perform the matrix operation <code>b = a*b</code>.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="a">a</td><td class="desc"> <p>A pointer to matrix <code>a</code>.</p> </td></tr> </table> <h4>inout</h4> <table class="fields"> <tr><td class="val" id="b">b</td><td class="desc"> <p>A pointer to matrix <code>b</code>.</p> </td></tr> </table> <h4>note</h4> <p>The result is undefined if either <code>a</code> or <code>b</code> is zero.</p> <p>Since the function uses wrap-around arithmetic, results become meaningless if the arguments are very large.</p> <hr> <h2 id="ft_matrix_invert">FT_Matrix_Invert<a class="headerlink" href="#ft_matrix_invert" title="Permanent link">¶</a></h2> <p>Defined in FT_GLYPH_H (freetype/ftglyph.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_error">FT_Error</a> ) <b>FT_Matrix_Invert</b>( <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* matrix ); </code></pre></div> <p>Invert a 2x2 matrix. Return an error if it can't be inverted.</p> <h4>inout</h4> <table class="fields"> <tr><td class="val" id="matrix">matrix</td><td class="desc"> <p>A pointer to the target matrix. Remains untouched in case of error.</p> </td></tr> </table> <h4>return</h4> <p>FreeType error code. 0 means success.</p> <hr> <h2 id="ft_angle">FT_Angle<a class="headerlink" href="#ft_angle" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> <span class="keyword">typedef</span> <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> <b>FT_Angle</b>; </code></pre></div> <p>This type is used to model angle values in FreeType. Note that the angle is a 16.16 fixed-point value expressed in degrees.</p> <hr> <h2 id="ft_angle_pi">FT_ANGLE_PI<a class="headerlink" href="#ft_angle_pi" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI</b> ( 180L << 16 ) </code></pre></div> <p>The angle pi expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p> <hr> <h2 id="ft_angle_2pi">FT_ANGLE_2PI<a class="headerlink" href="#ft_angle_2pi" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_2PI</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> * 2 ) </code></pre></div> <p>The angle 2*pi expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p> <hr> <h2 id="ft_angle_pi2">FT_ANGLE_PI2<a class="headerlink" href="#ft_angle_pi2" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI2</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> / 2 ) </code></pre></div> <p>The angle pi/2 expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p> <hr> <h2 id="ft_angle_pi4">FT_ANGLE_PI4<a class="headerlink" href="#ft_angle_pi4" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI4</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> / 4 ) </code></pre></div> <p>The angle pi/4 expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p> <hr> <h2 id="ft_sin">FT_Sin<a class="headerlink" href="#ft_sin" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_Sin</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Return the sinus of a given angle in fixed-point format.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The input angle.</p> </td></tr> </table> <h4>return</h4> <p>The sinus value.</p> <h4>note</h4> <p>If you need both the sinus and cosinus for a given angle, use the function <code><a href="ft2-computations.html#ft_vector_unit">FT_Vector_Unit</a></code>.</p> <hr> <h2 id="ft_cos">FT_Cos<a class="headerlink" href="#ft_cos" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_Cos</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Return the cosinus of a given angle in fixed-point format.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The input angle.</p> </td></tr> </table> <h4>return</h4> <p>The cosinus value.</p> <h4>note</h4> <p>If you need both the sinus and cosinus for a given angle, use the function <code><a href="ft2-computations.html#ft_vector_unit">FT_Vector_Unit</a></code>.</p> <hr> <h2 id="ft_tan">FT_Tan<a class="headerlink" href="#ft_tan" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_Tan</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Return the tangent of a given angle in fixed-point format.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The input angle.</p> </td></tr> </table> <h4>return</h4> <p>The tangent value.</p> <hr> <h2 id="ft_atan2">FT_Atan2<a class="headerlink" href="#ft_atan2" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-computations.html#ft_angle">FT_Angle</a> ) <b>FT_Atan2</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> x, <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> y ); </code></pre></div> <p>Return the arc-tangent corresponding to a given vector (x,y) in the 2d plane.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="x">x</td><td class="desc"> <p>The horizontal vector coordinate.</p> </td></tr> <tr><td class="val" id="y">y</td><td class="desc"> <p>The vertical vector coordinate.</p> </td></tr> </table> <h4>return</h4> <p>The arc-tangent value (i.e. angle).</p> <hr> <h2 id="ft_angle_diff">FT_Angle_Diff<a class="headerlink" href="#ft_angle_diff" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-computations.html#ft_angle">FT_Angle</a> ) <b>FT_Angle_Diff</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle1, <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle2 ); </code></pre></div> <p>Return the difference between two angles. The result is always constrained to the ]-PI..PI] interval.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle1">angle1</td><td class="desc"> <p>First angle.</p> </td></tr> <tr><td class="val" id="angle2">angle2</td><td class="desc"> <p>Second angle.</p> </td></tr> </table> <h4>return</h4> <p>Constrained value of <code>angle2-angle1</code>.</p> <hr> <h2 id="ft_vector_unit">FT_Vector_Unit<a class="headerlink" href="#ft_vector_unit" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Vector_Unit</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec, <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Return the unit vector corresponding to a given angle. After the call, the value of <code>vec.x</code> will be <code>cos(angle)</code>, and the value of <code>vec.y</code> will be <code>sin(angle)</code>.</p> <p>This function is useful to retrieve both the sinus and cosinus of a given angle quickly.</p> <h4>output</h4> <table class="fields"> <tr><td class="val" id="vec">vec</td><td class="desc"> <p>The address of target vector.</p> </td></tr> </table> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The input angle.</p> </td></tr> </table> <hr> <h2 id="ft_vector_rotate">FT_Vector_Rotate<a class="headerlink" href="#ft_vector_rotate" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Vector_Rotate</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec, <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Rotate a vector by a given angle.</p> <h4>inout</h4> <table class="fields"> <tr><td class="val" id="vec">vec</td><td class="desc"> <p>The address of target vector.</p> </td></tr> </table> <h4>input</h4> <table class="fields"> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The input angle.</p> </td></tr> </table> <hr> <h2 id="ft_vector_length">FT_Vector_Length<a class="headerlink" href="#ft_vector_length" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> ) <b>FT_Vector_Length</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec ); </code></pre></div> <p>Return the length of a given vector.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="vec">vec</td><td class="desc"> <p>The address of target vector.</p> </td></tr> </table> <h4>return</h4> <p>The vector length, expressed in the same units that the original vector coordinates.</p> <hr> <h2 id="ft_vector_polarize">FT_Vector_Polarize<a class="headerlink" href="#ft_vector_polarize" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Vector_Polarize</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec, <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> *length, <a href="ft2-computations.html#ft_angle">FT_Angle</a> *angle ); </code></pre></div> <p>Compute both the length and angle of a given vector.</p> <h4>input</h4> <table class="fields"> <tr><td class="val" id="vec">vec</td><td class="desc"> <p>The address of source vector.</p> </td></tr> </table> <h4>output</h4> <table class="fields"> <tr><td class="val" id="length">length</td><td class="desc"> <p>The vector length.</p> </td></tr> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The vector angle.</p> </td></tr> </table> <hr> <h2 id="ft_vector_from_polar">FT_Vector_From_Polar<a class="headerlink" href="#ft_vector_from_polar" title="Permanent link">¶</a></h2> <p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p> <div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> ) <b>FT_Vector_From_Polar</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec, <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> length, <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle ); </code></pre></div> <p>Compute vector coordinates from a length and angle.</p> <h4>output</h4> <table class="fields"> <tr><td class="val" id="vec">vec</td><td class="desc"> <p>The address of source vector.</p> </td></tr> </table> <h4>input</h4> <table class="fields"> <tr><td class="val" id="length">length</td><td class="desc"> <p>The vector length.</p> </td></tr> <tr><td class="val" id="angle">angle</td><td class="desc"> <p>The vector angle.</p> </td></tr> </table> <hr> </article> </div> </div> </main> <footer class="md-footer"> <div class="md-footer-nav"> <nav class="md-footer-nav__inner md-grid"> <a href="ft2-cache_subsystem.html" title="Cache Sub-System" class="md-flex md-footer-nav__link md-footer-nav__link--prev" rel="prev"> <div class="md-flex__cell md-flex__cell--shrink"> <i class="md-icon md-icon--arrow-back md-footer-nav__button"></i> </div> <div class="md-flex__cell md-flex__cell--stretch md-footer-nav__title"> <span class="md-flex__ellipsis"> <span class="md-footer-nav__direction"> Previous </span> Cache Sub-System </span> </div> </a> <a href="ft2-list_processing.html" title="List Processing" class="md-flex md-footer-nav__link md-footer-nav__link--next" rel="next"> <div class="md-flex__cell md-flex__cell--stretch md-footer-nav__title"> <span class="md-flex__ellipsis"> <span class="md-footer-nav__direction"> Next </span> List Processing </span> </div> <div class="md-flex__cell md-flex__cell--shrink"> <i class="md-icon md-icon--arrow-forward md-footer-nav__button"></i> </div> </a> </nav> </div> <div class="md-footer-meta md-typeset"> <div class="md-footer-meta__inner md-grid"> <div class="md-footer-copyright"> <div class="md-footer-copyright__highlight"> Copyright 2020 <a href = "https://www.freetype.org/license.html">The FreeType Project</a>. </div> powered by <a href="https://www.mkdocs.org" target="_blank" rel="noopener">MkDocs</a> and <a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener"> Material for MkDocs</a> </div> </div> </div> </footer> </div> <script src="assets/javascripts/application.c33a9706.js"></script> <script>app.initialize({version:"1.1",url:{base:"."}})</script> <script src="javascripts/extra.js"></script> </body> </html>